On the Number of Representations of an Integer by a Linear Form
Gil Alon and Pete L. Clark
1126 Burnside Hall
Department of Mathematics and Statistics
805 Sherbrooke West
Montreal, QC H3A 2K6
be positive integers generating the unit
be a residue class modulo
. It is known that the function
counts solutions to the equation
is a polynomial when restricted to
. Here we give, in the
, exact formulas for these polynomials up to the
constant terms, and exact formulas including the constants for
residue classes. The case
plays a special
role, and it is studied in more detail.
Full version: pdf,
Received June 23 2005;
revised version received October 19 2005.
Published in Journal of Integer Sequences October 20 2005.
Journal of Integer Sequences home page